Describing the set of words generated by interval exchange transformation

Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.Comment: 17 pages, this paper was submitted at scientific council of MSU, date: September 21, 200

N-block presentations and decidability of direct conjugacy between Subshifts of Finite Type

We consider the problem of inverting the transformation which consists in replacing a word by the sequence of its blocks of length N, i.e. its so-called N-block presentation. It was previously shown that among all the possible preimages of an N-block presentation, there exists a particular one which is maximal in the sense that all the other preimages can be obtained from it by letter to letter applications. We give here a combinatorial characterization of the maximal preimages of N-block presentations. Using this characterization, we show that, being given two subshifts of finite type X and Y, the existence of two numbers N and M such that the N-block presentation of X is similar to the M-block presentation of Y, which implies that X and Y are conjugate, is decidable.Comment: 14 pages, 2 figure

The prime spectrum of algebras of quadratic growth

We study prime algebras of quadratic growth. Our first result is that if $A$ is a prime monomial algebra of quadratic growth then $A$ has finitely many prime ideals $P$ such that $A/P$ has GK dimension one. This shows that prime monomial algebras of quadratic growth have bounded matrix images. We next show that a prime graded algebra of quadratic growth has the property that the intersection of the nonzero prime ideals $P$ such that $A/P$ has GK dimension 2 is non-empty, provided there is at least one such ideal. From this we conclude that a prime monomial algebra of quadratic growth is either primitive or has nonzero locally nilpotent Jacobson radical. Finally, we show that there exists a prime monomial algebra $A$ of GK dimension two with unbounded matrix images and thus the quadratic growth hypothesis is necessary to conclude that there are only finitely many prime ideals such that $A/P$ has GK dimension 1.Comment: 23 page